How do you find a unit vector from the point P=(1,1) and toward the point Q=(4,5)? Find a vector of length 15 pointing in the same direction.

1 Answer
May 3, 2018

The position vector of point P #(1,1)# will be

#vecP=hati+hatj#

And the position vector of point Q #(4,5)# will be

#vecQ=4hati+5hatj#

The vector from P to Q

#vec(PQ)=vecQ-vecP=3hati+4hatj#

The unit vector of #vec(PQ)#

#=vec(PQ)/absvec(PQ)#

#=(3hati+4hatj)/sqrt(3^2+4^2)#

#=(3hati+4hatj)/5#

So the vector of length 15 pointing in the direction of #vec(PQ)# will be.

#=15*(3hati+4hatj)/5#

#=3(3hati+4hatj)#

#=9hati+12hatj#